Developing a novel structured mesh generation method based on deep neural networks

In this paper, we develop a novel structured mesh generation method, MeshNet. The core of the proposed method is the introduction of deep neural networks to learn high-quality meshing rules and generate desired meshes. To accomplish this, MeshNet employs a well-designed physics-informed neural network to approximate the potential transformation (mapping) between computational and physical domains. The training process is governed by differential equations, boundary conditions, and a priori data derived from coarse mesh generation, which has been disregarded in previous studies. The automatic subdivision of a given domain into quadrilateral elements is achieved through efficient feed-forward neural prediction. A series of experiments are conducted to investigate the robustness of the proposed method. The results across different cases demonstrate that MeshNet is fast and robust. It outperforms state-of-the-art neural network-based generators and produces meshes of comparable or higher quality compared to expensive traditional meshing methods. Furthermore, the proposed method enables fast varisized mesh generation without re-training. The simplicity and computational efficiency of MeshNet make it a novel meshing tool in the discretization part of simulation software.